Determine confidence interval estimate of population mean

Question

Assignment:

Question 1

Part a)

Find the following probabilities by checking the z table

i) P(-1.5

ii) P((1.15

iii) Z_0.35

Part b)

Battery manufacturers compete on the basis of the amount of time their products last in cameras and toys. A manufacturer of alkaline batteries has observed that its batteries last for an average 26 hours when used in a toy racing car. The amount of time is normally distributed with a standard division of 2.5 hours.

i) What is the probability that the battery lasts between 25 and 29 hours?

ii) What is the probability that the battery lasts longer than 29 hours

iii) What is the probability that the battery lasts less than 25 hours.

Question 2

Part a)

A sample of n=25 observations is drawn from a normal population with µ=100 and σ=20. Find the following.

i) P(X¯<96)

ii) P(96

Part b)

The amount of time the university professors devote to their jobs per week is normally distributed with a mean of 52 hours and a  standard deviation of 6 hours.

i) What is the probability that a professor works for more than 60 hours per weeks?

ii) Find the probability that the mean amount of work per week for three randomly selected professors is more than 60 hours?

Question 3

Part a)

Given the following information X¯ =500, σ=12, n=50

i) Determine the 95% confidence interval estimate of population mean.

ii) Determine the 99% confidence interval estimate of population mean.

Part b)

A statistics practitioner calculated the mean and standard deviation from a sample of 51. They are X¯ =120 and s=15.

(i) Estimate the population mean with 95% confidence level.

(ii) Estimate the population mean with 99% confidence level.

Question 4

Part a)

Calculate the statistic, set up the rejection region, interpret the result, and draw the sampling distribution.

Part b)

H₀: µ=10

H₁: µ≠10

Given that: σ=10, n=100, X¯ =10, α=0.05.

A statistics practitioner is in the process of testing to determine whether is enough evidence to infer that the population mean is different from 180. She calculated the mean and standard deviation of a sample of 200 observations as X¯ =175 and s=22. Calculate the value of the test statistic of the test required to determine whether there is enough evidence to infer at the 5% significance level that the population mean is different from 180.